The movie isn't an analogy to chess. The movie is about the illusion that imprisons every one of us.
Deep beneath the films violence, blood and grit, lurks a spiritual and enlightening message - a message echoed throughout time by revered figures such as Buddha and Bodhidharma, a message also echoed in Kabbalah (which is probably where Guy Ritchie drew his inspiration from, as his then-wife, Madonna, is heavily into Kabbalah). And that message is this: we are not our ego; the ego, far from being our friend, is responsible for most of our pain and misery; the ego is a product of the mind and creates the illusion of separation, the ego is a prison, a prison that very few people recognise as such.
To answer your question: Mr. Gold is everyone's ego. In Jake's case, Mr. Gold is the part of Jake who wants to kill Macha.